"It definitely feels good," Grisham said. "Everybody in here has been waiting -- not if, but when, when it's going to come around. It's nice to stack two days like that on top of each other."
Darvish (5-4) earned the benchmark victory after allowing four earned runs and five hits while striking out six and walking four in 5⅓ innings.
"It means a lot," Darvish said. "It just tells you that I've been able to play this long and go into battle with my teammates."
Jake Cronenworth had his second-consecutive three-hit game for San Diego after batting just .198 in his first 60 games of the season. After missing the past four games while tending to soreness in his left wrist, Xander Bogaerts had two runs and two hits, including his first double since May 14.
Machado's two-run homer, which spearheaded a three-run first inning for the Padres, was his first since May 9 and a 425-foot solo shot from Tatis was his team-leading 12th of the season. Sanchez's two-run homer in the second inning was his fifth since joining San Diego on May 30 while Dixon's was just his second of the season.
"A lot of times, you get a little confidence again and you do some things you've done in the past," Padres manager Bob Melvin said of Sanchez. "He's still a young man for what he does. Each and every game he has like this, you'll see some of the potential he's always had."
Josh Hader picked up his 14th save of the season after forcing Elias Díaz to ground into a force out with runners on first and third.
The loss was Colorado's fifth in a row -- its second-longest drought of the season -- and its ninth in 11 games. The Rockies have now lost 14 of their past 15 games against NL West teams, including each eight straight.
Starter Austin Gomber (4-5) took the loss for the Rockies, giving up seven earned runs and 11 hits -- including three homers -- over four innings. He struggled with his fastball, as each of the three home runs he surrendered came on four-seam pitches. Over his past five starts, he has given up 23 earned runs in 20⅔ innings.
"Two pitches to Fernando, first-pitch single by (Juan) Soto, first-pitch homer by Machado. Four pitches to three hitters, that's pretty quick," Gomber said. "But that can work in your favor, too -- I've had nights where you have five-pitch innings, right? You've just got to make better pitches. If guys are going to swing, that's great, but you've got to execute when they have that approach."
Mike Moustakas had two hits for Colorado, including a 441-foot, two-run home run in the eighth inning.